The field of the invention is AC induction motor drives and more specifically the area of injecting high frequency voltage signals into an AC induction motor and using high frequency feedback signals to identify stator flux position.
Induction motors have broad application in industry, particularly when large horsepower is needed. In a three-phase induction motor, three phase alternating voltages are impressed across three separate motor stator windings and cause three phase currents therein. Because of inductances, the three currents typically lag the voltages by some phase angle. The three currents produce a rotating magnetic stator field. A rotor contained within the stator field experiences an induced current (hence the term “induction”) which generates a rotor field. The rotor field typically lags the stator field by some phase angle. The rotor field is attracted to the rotating stator field and the interaction between the two fields causes the rotor to rotate.
A common rotor design includes a “squirrel cage winding” in which axial conductive bars are connected at either end by shorting rings to form a generally cylindrical structure. The flux of the stator field cutting across the conductive bars induces cyclic current flows through the bars and across the shorting rings. The cyclic current flows in turn produce the rotor field. The use of this induced current to generate the rotor field eliminates the need for slip rings or brushes to provide power to the rotor, making the design relatively maintenance free.
To a first approximation, the torque and speed of an induction motor may be controlled by changing the frequency of the driving voltage and thus the angular rate of the rotating stator field. Generally, for a given torque, increasing the stator field rate will increase the speed of the rotor (which follows the stator field). Alternatively, for a given rotor speed, increasing the frequency of the stator field will increase the torque by increasing the slip, that is the difference in speed between the rotor and the stator fields. An increase in slip increases the rate at which flux lines are cut by the rotor, increasing the rotor generated field and thus the force or torque between the rotor and stator fields.
Referring to FIG. 1, a rotating phasor 1 corresponding to a stator magneto motive force (“mmf”) will generally have some angle a with respect to the phasor of rotor flux 2. The torque generated by the motor will be proportional to the magnitudes of these phasors 1 and 2 but also will be a function of their angle α. Maximum torque is produced when phasors 1 and 2 are at right angles to each other whereas zero torque is produced if the phasors are aligned. The stator mmf phasor 1 may therefore be usefully decomposed into a torque producing component 3 perpendicular to rotor flux phasor 2 and a flux component 4 parallel to rotor flux phasor 2.
These two components 3 and 4 of the stator mmf are proportional, respectively, to two stator current components: iq, a torque producing current, and id, a flux producing current, which may be represented by quadrature or orthogonal vectors in a rotating or synchronous frame of reference (i.e., a reference frame that rotates along with the stator flux vector) and each vector iq and id is characterized by slowly varying DC magnitude.
Accordingly, in controlling an induction motor, it is generally desired to control not only the frequency of the applied voltage (hence the speed of the rotation of the stator flux phasor 1), but also the phase of the applied voltage relative to the current flow and hence the division of the currents through the stator windings into the iq and id components. Control strategies that attempt to independently control current components iq and id are generally referred to as field oriented control strategies (“FOC”).
Generally, it is desirable to design FOC strategies that are capable of driving motors of many different designs and varying sizes. Such versatility cuts down on research, development, and manufacturing costs and also results in easily serviceable controllers. Unfortunately, while versatile controllers are cost-effective, FOC controllers cannot control motor operation precisely unless they can adjust the division of d and q-axis currents through the stator windings to account for motor-specific operating parameters. For this reason, in order to increase motor operating precision, various feedback loops are typically employed to monitor stator winding currents and voltages and/or motor speed. A controller uses feedback information to determine how the inverter supplied voltage must be altered to compensate for system disturbances due to system specific and often dynamic operating parameters and then adjusts control signals to supply the desired inverter voltages.
To this end, in an exemplary FOC system, two phase d and q-axis command currents are provided that are calculated to control a motor in a desired fashion. The command currents are compared to d and q-axis motor feedback currents to generate error signals (i.e., the differences between the command and feedback currents). The error signals are then used to generate d and q-axis command voltage signals which are in turn transformed into three phase command voltage signals, one voltage signal for each of the three motor phases. The command voltage signals are used to drive a pulse width modulated (PWM) inverter that generates voltages on three motor supply lines. To provide the d and q-axis current feedback signals the system typically includes current sensors to sense the three phase line currents and a coordinate transformation block is used to transform the three phase currents to two phase synchronous dq frame of reference feedback currents.
In addition to requiring two phase signals and three phase signals to perform 2-to-3 and 3-to-2 phase transformations, respectively, a precise flux position angle estimate θ′m is also required. One common way to generate a flux angle feedback estimate is to integrate a stator frequency. A stator frequency can be determined by adding a measured rotor frequency (rotor speed) and a calculated slip frequency. In the case of drives that do not include a rotor speed sensor, it is necessary to estimate both the rotor frequency and the slip frequency to determine the flux angle. Thus, these drives require precise knowledge of motor parameter values.
In an effort to reduce system costs and increase reliability, the controls industry has recently developed various types of sensorless or self-sensing induction machine systems that, as the labels imply, do not include dedicated speed sensing hardware and corresponding cabling but that, nevertheless, can generate accurate position, flux and velocity estimates. Techniques used for operating parameter estimation can be divided into two groups including techniques that track speed dependent phenomenon and techniques that track spatial saliencies in system signals. These techniques generally use disturbances in d and q-axis feedback currents to identify the operating parameters of interest and hence provide additional functionality which, in effect, “piggy-backs” on feedback signals that are obtained for another purpose (i.e., dq current components are already required for FOC).
Because speed dependent techniques depend on speed in order to generate an identifiable feedback signal, these techniques ultimately fail at zero or low (e.g., below 5 Hz) excitation frequency due to lack of signal. In addition, because these methods estimate operating parameters from voltage and current, these techniques are sensitive to temperature varying system parameters such as stator resistance, etc.
One type of saliency tracking technique includes injecting or applying a known high frequency “injection” voltage signal in addition to each of the command voltage signals used to drive the PWM inverter and using feedback current (or voltage) signals to identify saliencies associated with the flux angle. To this end, an exemplary system converts a high frequency command signal into a high frequency phase angle and generates a first injection signal that is the product of a scalar and the sine of the high frequency phase angle. Second and third injection signals are also generated, each of the second and third signals phase shifted from the first signal by 120 degrees. A separate one of the first, second and third signals is then added to a separate one of the three voltage command signals that are used to drive the PWM inverter.
One injection type saliency tracking algorithm to generate a flux position angle estimate without a rotor speed sensor employs a negative sequence of the high frequency current component and is described in an article that issued in the IEEE Transactions on Industry Applications publication, vol. 34, No. 5, September/October 1998 by Robert Lorenz which is entitled “Using Multiple Saliencies For The Estimation Of Flux Position, And Velocity In AC Machines” (hereinafter “the Lorenz article”). The algorithm in the Lorenz article is based on the fact that when a high frequency voltage signal (referred to in the Lorenz article as a “carrier signal”) is injected into a rotating system, a resulting high frequency field interacts with system saliency to produce a “carrier” signal current that contains information relating to the position of the saliency. The carrier current consists of both positive and negative-sequence components relative to the carrier signal voltage excitation. While the positive sequence component rotates in the same direction as the carrier signal voltage excitation and therefore contains no spatial information, the negative-sequence component contains spatial information in its phase. The Lorenz article teaches that the positive sequence component can be filtered off leaving only the negative-sequence component which can be fed to an observer used to extract flux angle position information.
Unfortunately, algorithms like the algorithm described in the Lorenz article only works well if an induction machine is characterized by a single sinusoidally distributed spatial saliency. As known in the art, in reality, motor currents exhibit more than a single spatial saliency in part due to the fact that PWM inverters produce a plethora of harmonics. As a result, the phase current negative sequence comprises a complicated spectrum that renders the method described in the Lorenz article relatively inaccurate.
Injection type saliency tracking algorithms employ a zero sequence high frequency current or voltage component instead of the negative sequence current component. One such technique is described in an article that issued in the IEEE IAS publication, pp. 2290–2297, Oct. 3–7, 1999, Phoenix Ariz., which is entitled “A New Zero Frequency Flux Position Detection Approach For Direct Field Orientation Control Drives” (hereinafter “the Consoli article”). The Consoli article teaches that the main field of an induction machine saturates during system operation which causes the spatial distribution of the air gap flux to assume a flattened sinusoidal waveform including all odd harmonics and dominated by the third harmonic of the fundamental. The third harmonic flux component linking the stator windings induces a third harmonic voltage component (i.e., a voltage zero sequence) that is always orthogonal to the flux component and that can therefore be used to determine the flux position. Unfortunately, the third harmonic frequency is low band width and therefore not particularly suitable for instantaneous position determination needed for low speed control.
The Consoli article further teaches that where high frequency signals are injected into a rotating system, the injected signals produce a variation in the saturation level that depends on the relative positions of the main rotating field Fm and high frequency rotating field Fh. Due to the fundamental component of the main field Fm, the impedance presented to the high frequency injected signal varies in space and an unbalanced impedance system results. The Consoli article teaches that the unbalanced system produces a zero sequence voltage component that, in addition to including an injected frequency component and a fundamental zero sequence component, includes an additional component (hereinafter “the high frequency first harmonic component”) having an angular frequency represented by the following equation:ωh1zs=ωh±ω1  Eq. 1where:
ωh1zs=high frequency first harmonic component frequency;
ωh=high frequency injected signal frequency;
ω1=fundamental (i.e., first harmonic) stator frequency; and
where the sign “±” is negative if the high frequency “injected” signal has a direction that is the same as the fundamental field direction and is positive if the injected signal has a direction opposite the fundamental field direction.
In this case, referring to FIGS. 2a and 2b, an air gap flux component λhfzs associated with the high frequency first harmonic component and that results from complex interaction of the fundamental stator frequency component and the injected high frequency signal induces a high frequency first harmonic voltage component Vhfzs on the stator windings that always leads flux component λhfzs by 90°. Hereinafter additional voltage component Vhfzs will be referred to as the high frequency first harmonic voltage component and the additional flux component λhfzs will be referred to as the high frequency first harmonic flux component unless indicated otherwise. The maximum high frequency first harmonic flux component λhfzs always occurs when the main field Fm and high frequency rotating field Fh are aligned and in phase and the minimum high frequency first harmonic flux component λhfzs always occurs when the main field Fm and high frequency rotating field Fh are aligned but in opposite phase. Thus, in theory, by tracking the zero crossing points of the high frequency first harmonic voltage component Vhfzs and the instances when minimum and maximum values of the high frequency first harmonic voltage component Vhfzs occur, the angular position θh of the high frequency rotating field Fh can be used to determine the position θm of the main air gap flux.
For instance, referring to FIGS. 2a and 2b, and also to FIGS. 14 and 15, at time t1 (see FIG. 14) when voltage component Vhfzs is transitioning from positive to negative and crosses zero, main field Fm is in phase and aligned with the high frequency flux λhfzs (i.e., field Fh) which lags voltage Vhfzs by 90° and therefore main field angle θm can be determined by solving the equation θh−π/2 (where θh is the high frequency injected signal angle). As indicated in FIG. 2b, at time t1 high frequency first harmonic voltage component Vhfzs has a zero value. Nevertheless, in FIG. 14 voltage Vhfzs is illustrated as having a magnitude so that angle θh is illustrated as having a magnitude and angle θh can be illustrated. Similar comments are applicable to FIG. 15 and time t3.
At time t2 where voltage Vhfzs reaches a minimum value, main field Fm and flux λhfzs are in quadrature and therefore main field angle θm can be expressed as θh−π (i.e., 90° between signal Vhfzs and flux λhfzs and another 90° between flux λhfzs and main field Fm for a total of π). At time t3 (see FIG. 15) where voltage Vhfzs is transitioning from negative to positive through zero, the main field is out of phase with flux component λhfzs and therefore main field angle θm can be expressed as θh−3π/2. Similarly, at time t4 voltage Vhfzs reaches a maximum value with the main field Fm and flux component λhfzs (i.e., field Fh) again in quadrature and main field Fm leading flux component λhfzs and therefore main field angle θm is equal to high frequency angel θh. Thus, where the high frequency first harmonic voltage component (i.e., the component having a frequency equal to the sum of the injected signal frequency and the fundamental stator frequency) can be extracted, Consoli teaches that the main field angle θm is determinable.
To extract the high frequency first harmonic voltage component Consoli teaches that a band pass filter may be employed. Here, the filter would be tuned to have a bandwidth substantially centered on the injected signal frequency so that high frequency signals within a few Hz (e.g., within 10 Hz) of the injected signal frequency could be identified. Thus, for instance, where the injected signal frequency is 200 Hz, the band pass filter may have cutoff frequencies of 190 Hz and 210 Hz.
While the Consoli type system operates well in theory, in reality, the high frequency first harmonic signal required by Consoli is difficult to extract in a practical manner. Extraction of the high frequency first harmonic is complicated by a number of factors. First, the amplitude of any particular signal within the frequency pass band of interest (e.g., a frequency range centered on the injected signal frequency) is typically 10 to 100 times smaller than the carrier frequency in the zero sequence voltage feedback signal. A relatively high order (e.g., 4th, 8th, etc.) band pass filter has typically been required to sufficiently attenuate the carrier frequency, the fundamental frequency and its harmonics, line harmonics, and other spurious noise within the zero sequence feedback signal.
As the order of the bandpass filter is increased, the phase shift associated with the filter bandwidth frequencies increases appreciably and may de-stabilize a control system. To this end, FIG. 3 illustrates amplitude and phase waveforms 510 and 512 of a typical high order (e.g., 4th order or greater) IIR bandpass filter. As illustrated, approximately 30% of the filter bandwidth centered on the injected signal frequency is utilized by an encoderless AC drive system. Hereinafter, the utilized 30% of the pass band or the pass band of interest (PBI) will be referenced by numeral 514. Referring specifically to the section of phase waveform 512 within PBI 514, there is significant phase variation 518 at different PBI frequencies. Thus, for instance, where the injected signal frequency is 200 Hz and the high frequency first harmonic component is at 201 Hz, the phase shift may be 20 degrees. Here, if the high frequency first harmonic is used to identify the main field flux position, the estimated main field flux position may be off by 20 degrees. Complicating matters further, as the fundamental stator frequency is altered (e.g., form 1 Hz to 2 Hz), the altered fundamental will cause a different phase shift. For instance, where the injected signal frequency is 200 Hz and the high frequency first harmonic component is at 202 Hz (i.e., the fundamental stator frequency is changed form 1 Hz to 2 Hz), the phase shift may be 50 degrees instead of 20 degrees.
Second, even if a filter were designed that had acceptable phase shift within the PBI, as in the case of the negative current component employed by Lorenz, high frequency zero sequence feedback signals within the PBI are typically characterized by a complicated harmonic spectrum. In this regard, see FIG. 9 which illustrates an exemplary zero sequence voltage feedback signal Vzs. In FIG. 9 the ratio of carrier frequency to high injected signal frequency is approximately 14 to 1. Thus, if the carrier frequency was 2800 Hz, the injected frequency would be approximately 200 Hz. Hereinafter an injected frequency of 200 Hz will be assumed unless indicated otherwise.
FIG. 4 includes a graph illustrating an exemplary frequency spectrum that was generated for a zero sequence voltage feedback signal like signal Vzs illustrated in FIG. 9. The portion of the frequency spectrum illustrated only includes the frequencies within a PBI centered on a 200 Hz injected frequency (e.g., from approximately 196 to 204 Hz) where the fundamental stator frequency was 0.5781 Hz. In FIG. 4, spike 500 corresponds to the injected frequency component (e.g., 200 Hz), spike 502 corresponds to the high frequency first harmonic component (e.g., 199.4219 Hz), spike 504 corresponds to the high frequency second harmonic component and spike 506 corresponds to the high frequency fourth harmonic. Clearly, within PBI 514, high frequency first harmonic component 502 is dominated by the injected frequency component 500, the high frequency second harmonic component 504 and the high frequency fourth harmonic component 506. In fact, the dominant second harmonic component 504 has an amplitude that is more than 20 times the amplitude of the high frequency first harmonic component 502.
Referring again to FIG. 4, relative amplitudes of the high frequency harmonic components within the PBI complicate the task of extracting the high frequency first harmonic. In addition, the close spatial proximities of the high frequency components, particularly at low frequencies, render it impractical to isolate the high frequency first harmonic component using a single high order band pass filter.